Allocating a fixed cost across decision-making units with undesirable outputs: A bargaining game approach

Allocating a fixed cost among a set of peer decision-making units (DMUs) is one of the most important applications of data envelopment analysis. However, almost all existing studies have addressed the fixed cost allocation (FCA) problem within a traditional framework while ignoring the existence of undesirable outputs. Undesirable outputs are neither scarce in various production activities in real world applications nor trivial in efficiency evaluation and subsequent decision making. Motivated by this observation, this article attempts to explicitly extend the traditional FCA problem to situations in which DMUs are necessarily involved with undesirable outputs. To this end, we first investigate the efficiency evaluation of DMUs considering undesirable outputs based on the joint weak disposability assumption. Then, flexible FCA schemes are considered to revisit the efficiency evaluation process. The results show that feasible allocation schemes exist such that all DMUs can be simultaneously efficient. Furthermore, we define the comprehensive satisfaction degree and develop a satisfaction degree bargaining game approach to determine a unique FCA scheme. Finally, the proposed approach is tested with an empirical study of banking activities based on real conditions.